Question

Given f(x) = `1/(x - 1)`. Find the points of discontinuity of the composite function y = f[f(x)]

Answer 1

We know that f(x) = `1/(x - 1)` is discontinuous at x = 1

Now, for x ≠ 1,

f(f(x)) = `"f"(1/(x - 1))`

= `1/(1/(x - 1) - 1)`

= `(x - 1)/(2 - x)`.

Which is discontinuous at x = 2.

Hence, the points of discontinuity are x = 1 and x = 2.